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  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "e3d9fbe2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import xlrd\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f8b7f7c6",
   "metadata": {
    "collapsed": true
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>timestamp</th>\n",
       "      <th>group</th>\n",
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       "      <td>2017-01-12 00:51:57.078372</td>\n",
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       "      <td>2017-01-15 01:20:28.957438</td>\n",
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       "    <tr>\n",
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       "      <td>715931</td>\n",
       "      <td>2017-01-16 12:40:24.467417</td>\n",
       "      <td>treatment</td>\n",
       "      <td>new_page</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>294478 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        user_id                   timestamp      group landing_page  converted\n",
       "0        851104  2017-01-21 22:11:48.556739    control     old_page          0\n",
       "1        804228  2017-01-12 08:01:45.159739    control     old_page          0\n",
       "2        661590  2017-01-11 16:55:06.154213  treatment     new_page          0\n",
       "3        853541  2017-01-08 18:28:03.143765  treatment     new_page          0\n",
       "4        864975  2017-01-21 01:52:26.210827    control     old_page          1\n",
       "...         ...                         ...        ...          ...        ...\n",
       "294473   751197  2017-01-03 22:28:38.630509    control     old_page          0\n",
       "294474   945152  2017-01-12 00:51:57.078372    control     old_page          0\n",
       "294475   734608  2017-01-22 11:45:03.439544    control     old_page          0\n",
       "294476   697314  2017-01-15 01:20:28.957438    control     old_page          0\n",
       "294477   715931  2017-01-16 12:40:24.467417  treatment     new_page          0\n",
       "\n",
       "[294478 rows x 5 columns]"
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     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1=pd.read_csv('C:/Users/Mr.Xiao/Desktop/ab_data.csv')\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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       " '2017-01-17 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-21 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-24 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-20 ',\n",
       " ...]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "date=[]\n",
    "for i in df1['timestamp']:\n",
    "#     print(i[:11])\n",
    "    date.append(i[:11])\n",
    "date"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f99132e5",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['2017-01-21 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-21 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-21 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-24 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-24 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-03 ',\n",
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       " '2017-01-17 ',\n",
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       " '2017-01-09 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-19 ',\n",
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       " '2017-01-19 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-07 ',\n",
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       " '2017-01-17 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-16 ',\n",
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       " '2017-01-17 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-09 ',\n",
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       " '2017-01-17 ',\n",
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       " '2017-01-13 ',\n",
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       " '2017-01-20 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-21 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-21 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-21 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-16 ',\n",
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       " '2017-01-14 ',\n",
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       " '2017-01-07 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-04 ',\n",
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       " '2017-01-10 ',\n",
       " '2017-01-15 ',\n",
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       " '2017-01-20 ',\n",
       " '2017-01-04 ',\n",
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       " '2017-01-13 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-13 ',\n",
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       " '2017-01-08 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-07 ',\n",
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       " '2017-01-02 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-05 ',\n",
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       " '2017-01-03 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-21 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-21 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-24 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-24 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-21 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-24 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-24 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-18 ',\n",
       " '2017-01-24 ',\n",
       " '2017-01-10 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-09 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-21 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-15 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-02 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-07 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-12 ',\n",
       " '2017-01-24 ',\n",
       " '2017-01-08 ',\n",
       " '2017-01-05 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-04 ',\n",
       " '2017-01-19 ',\n",
       " '2017-01-14 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-11 ',\n",
       " '2017-01-23 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-13 ',\n",
       " '2017-01-06 ',\n",
       " '2017-01-22 ',\n",
       " '2017-01-17 ',\n",
       " '2017-01-16 ',\n",
       " '2017-01-20 ',\n",
       " '2017-01-03 ',\n",
       " '2017-01-04 ',\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
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       "    <tr>\n",
       "      <th>landing_page</th>\n",
       "      <th>day</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th rowspan=\"23\" valign=\"top\">new_page</th>\n",
       "      <th>2017-01-02</th>\n",
       "      <td>2280019518</td>\n",
       "      <td>345</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-03</th>\n",
       "      <td>5301546898</td>\n",
       "      <td>763</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-04</th>\n",
       "      <td>5208732855</td>\n",
       "      <td>771</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-05</th>\n",
       "      <td>5206556401</td>\n",
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       "      <th>2017-01-06</th>\n",
       "      <td>5369184894</td>\n",
       "      <td>849</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-07</th>\n",
       "      <td>5273072817</td>\n",
       "      <td>774</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-08</th>\n",
       "      <td>5351331929</td>\n",
       "      <td>819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-09</th>\n",
       "      <td>5280785580</td>\n",
       "      <td>794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-10</th>\n",
       "      <td>5337140734</td>\n",
       "      <td>858</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-11</th>\n",
       "      <td>5341632838</td>\n",
       "      <td>781</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-12</th>\n",
       "      <td>5288063167</td>\n",
       "      <td>825</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-13</th>\n",
       "      <td>5192021120</td>\n",
       "      <td>737</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-14</th>\n",
       "      <td>5275635725</td>\n",
       "      <td>799</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-15</th>\n",
       "      <td>5227769948</td>\n",
       "      <td>757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-16</th>\n",
       "      <td>5238182901</td>\n",
       "      <td>793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-17</th>\n",
       "      <td>5208691027</td>\n",
       "      <td>837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-18</th>\n",
       "      <td>5273651231</td>\n",
       "      <td>835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-19</th>\n",
       "      <td>5240533967</td>\n",
       "      <td>774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-20</th>\n",
       "      <td>5327531244</td>\n",
       "      <td>796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-21</th>\n",
       "      <td>5229118905</td>\n",
       "      <td>768</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-22</th>\n",
       "      <td>5309354179</td>\n",
       "      <td>797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-23</th>\n",
       "      <td>5289419103</td>\n",
       "      <td>813</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-24</th>\n",
       "      <td>2946206476</td>\n",
       "      <td>456</td>\n",
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       "    <tr>\n",
       "      <th rowspan=\"23\" valign=\"top\">old_page</th>\n",
       "      <th>2017-01-02</th>\n",
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       "      <td>365</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-03</th>\n",
       "      <td>5280566202</td>\n",
       "      <td>759</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-04</th>\n",
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       "      <td>812</td>\n",
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       "    <tr>\n",
       "      <th>2017-01-05</th>\n",
       "      <td>5128705666</td>\n",
       "      <td>802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-06</th>\n",
       "      <td>5298157982</td>\n",
       "      <td>777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-07</th>\n",
       "      <td>5272498943</td>\n",
       "      <td>807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-08</th>\n",
       "      <td>5345890950</td>\n",
       "      <td>807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-09</th>\n",
       "      <td>5298850362</td>\n",
       "      <td>806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-10</th>\n",
       "      <td>5305770106</td>\n",
       "      <td>763</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-11</th>\n",
       "      <td>5330304240</td>\n",
       "      <td>812</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-12</th>\n",
       "      <td>5198958382</td>\n",
       "      <td>804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-13</th>\n",
       "      <td>5231560346</td>\n",
       "      <td>776</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-14</th>\n",
       "      <td>5234273795</td>\n",
       "      <td>842</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-15</th>\n",
       "      <td>5361729544</td>\n",
       "      <td>823</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-16</th>\n",
       "      <td>5278947602</td>\n",
       "      <td>818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-17</th>\n",
       "      <td>5280311328</td>\n",
       "      <td>825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-18</th>\n",
       "      <td>5180179694</td>\n",
       "      <td>820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-19</th>\n",
       "      <td>5244446753</td>\n",
       "      <td>801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-20</th>\n",
       "      <td>5210530591</td>\n",
       "      <td>764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-21</th>\n",
       "      <td>5394483345</td>\n",
       "      <td>863</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-22</th>\n",
       "      <td>5264663023</td>\n",
       "      <td>794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-23</th>\n",
       "      <td>5355468165</td>\n",
       "      <td>855</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-24</th>\n",
       "      <td>2998264745</td>\n",
       "      <td>444</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             user_id  converted\n",
       "landing_page day                               \n",
       "new_page     2017-01-02   2280019518        345\n",
       "             2017-01-03   5301546898        763\n",
       "             2017-01-04   5208732855        771\n",
       "             2017-01-05   5206556401        757\n",
       "             2017-01-06   5369184894        849\n",
       "             2017-01-07   5273072817        774\n",
       "             2017-01-08   5351331929        819\n",
       "             2017-01-09   5280785580        794\n",
       "             2017-01-10   5337140734        858\n",
       "             2017-01-11   5341632838        781\n",
       "             2017-01-12   5288063167        825\n",
       "             2017-01-13   5192021120        737\n",
       "             2017-01-14   5275635725        799\n",
       "             2017-01-15   5227769948        757\n",
       "             2017-01-16   5238182901        793\n",
       "             2017-01-17   5208691027        837\n",
       "             2017-01-18   5273651231        835\n",
       "             2017-01-19   5240533967        774\n",
       "             2017-01-20   5327531244        796\n",
       "             2017-01-21   5229118905        768\n",
       "             2017-01-22   5309354179        797\n",
       "             2017-01-23   5289419103        813\n",
       "             2017-01-24   2946206476        456\n",
       "old_page     2017-01-02   2288199591        365\n",
       "             2017-01-03   5280566202        759\n",
       "             2017-01-04   5262099491        812\n",
       "             2017-01-05   5128705666        802\n",
       "             2017-01-06   5298157982        777\n",
       "             2017-01-07   5272498943        807\n",
       "             2017-01-08   5345890950        807\n",
       "             2017-01-09   5298850362        806\n",
       "             2017-01-10   5305770106        763\n",
       "             2017-01-11   5330304240        812\n",
       "             2017-01-12   5198958382        804\n",
       "             2017-01-13   5231560346        776\n",
       "             2017-01-14   5234273795        842\n",
       "             2017-01-15   5361729544        823\n",
       "             2017-01-16   5278947602        818\n",
       "             2017-01-17   5280311328        825\n",
       "             2017-01-18   5180179694        820\n",
       "             2017-01-19   5244446753        801\n",
       "             2017-01-20   5210530591        764\n",
       "             2017-01-21   5394483345        863\n",
       "             2017-01-22   5264663023        794\n",
       "             2017-01-23   5355468165        855\n",
       "             2017-01-24   2998264745        444"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.groupby(['landing_page','day']).sum('converted')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3c53159b",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
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       "      <th>2017-01-10</th>\n",
       "      <td>6736</td>\n",
       "      <td>6736</td>\n",
       "      <td>6736</td>\n",
       "      <td>6736</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-11</th>\n",
       "      <td>6781</td>\n",
       "      <td>6781</td>\n",
       "      <td>6781</td>\n",
       "      <td>6781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-12</th>\n",
       "      <td>6592</td>\n",
       "      <td>6592</td>\n",
       "      <td>6592</td>\n",
       "      <td>6592</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-13</th>\n",
       "      <td>6633</td>\n",
       "      <td>6633</td>\n",
       "      <td>6633</td>\n",
       "      <td>6633</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-14</th>\n",
       "      <td>6642</td>\n",
       "      <td>6642</td>\n",
       "      <td>6642</td>\n",
       "      <td>6642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-15</th>\n",
       "      <td>6805</td>\n",
       "      <td>6805</td>\n",
       "      <td>6805</td>\n",
       "      <td>6805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-16</th>\n",
       "      <td>6690</td>\n",
       "      <td>6690</td>\n",
       "      <td>6690</td>\n",
       "      <td>6690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-17</th>\n",
       "      <td>6710</td>\n",
       "      <td>6710</td>\n",
       "      <td>6710</td>\n",
       "      <td>6710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-18</th>\n",
       "      <td>6586</td>\n",
       "      <td>6586</td>\n",
       "      <td>6586</td>\n",
       "      <td>6586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-19</th>\n",
       "      <td>6654</td>\n",
       "      <td>6654</td>\n",
       "      <td>6654</td>\n",
       "      <td>6654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-20</th>\n",
       "      <td>6622</td>\n",
       "      <td>6622</td>\n",
       "      <td>6622</td>\n",
       "      <td>6622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-21</th>\n",
       "      <td>6841</td>\n",
       "      <td>6841</td>\n",
       "      <td>6841</td>\n",
       "      <td>6841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-22</th>\n",
       "      <td>6675</td>\n",
       "      <td>6675</td>\n",
       "      <td>6675</td>\n",
       "      <td>6675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-23</th>\n",
       "      <td>6811</td>\n",
       "      <td>6811</td>\n",
       "      <td>6811</td>\n",
       "      <td>6811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2017-01-24</th>\n",
       "      <td>3800</td>\n",
       "      <td>3800</td>\n",
       "      <td>3800</td>\n",
       "      <td>3800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          user_id  timestamp  group  converted\n",
       "landing_page day                                              \n",
       "new_page     2017-01-02      2888       2888   2888       2888\n",
       "             2017-01-03      6712       6712   6712       6712\n",
       "             2017-01-04      6618       6618   6618       6618\n",
       "             2017-01-05      6616       6616   6616       6616\n",
       "             2017-01-06      6825       6825   6825       6825\n",
       "             2017-01-07      6683       6683   6683       6683\n",
       "             2017-01-08      6782       6782   6782       6782\n",
       "             2017-01-09      6712       6712   6712       6712\n",
       "             2017-01-10      6787       6787   6787       6787\n",
       "             2017-01-11      6772       6772   6772       6772\n",
       "             2017-01-12      6730       6730   6730       6730\n",
       "             2017-01-13      6605       6605   6605       6605\n",
       "             2017-01-14      6687       6687   6687       6687\n",
       "             2017-01-15      6644       6644   6644       6644\n",
       "             2017-01-16      6637       6637   6637       6637\n",
       "             2017-01-17      6612       6612   6612       6612\n",
       "             2017-01-18      6699       6699   6699       6699\n",
       "             2017-01-19      6639       6639   6639       6639\n",
       "             2017-01-20      6771       6771   6771       6771\n",
       "             2017-01-21      6634       6634   6634       6634\n",
       "             2017-01-22      6748       6748   6748       6748\n",
       "             2017-01-23      6700       6700   6700       6700\n",
       "             2017-01-24      3738       3738   3738       3738\n",
       "old_page     2017-01-02      2895       2895   2895       2895\n",
       "             2017-01-03      6682       6682   6682       6682\n",
       "             2017-01-04      6666       6666   6666       6666\n",
       "             2017-01-05      6508       6508   6508       6508\n",
       "             2017-01-06      6703       6703   6703       6703\n",
       "             2017-01-07      6698       6698   6698       6698\n",
       "             2017-01-08      6782       6782   6782       6782\n",
       "             2017-01-09      6727       6727   6727       6727\n",
       "             2017-01-10      6736       6736   6736       6736\n",
       "             2017-01-11      6781       6781   6781       6781\n",
       "             2017-01-12      6592       6592   6592       6592\n",
       "             2017-01-13      6633       6633   6633       6633\n",
       "             2017-01-14      6642       6642   6642       6642\n",
       "             2017-01-15      6805       6805   6805       6805\n",
       "             2017-01-16      6690       6690   6690       6690\n",
       "             2017-01-17      6710       6710   6710       6710\n",
       "             2017-01-18      6586       6586   6586       6586\n",
       "             2017-01-19      6654       6654   6654       6654\n",
       "             2017-01-20      6622       6622   6622       6622\n",
       "             2017-01-21      6841       6841   6841       6841\n",
       "             2017-01-22      6675       6675   6675       6675\n",
       "             2017-01-23      6811       6811   6811       6811\n",
       "             2017-01-24      3800       3800   3800       3800"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1.groupby(['landing_page','day']).count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c28fbe3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha=0.05\n",
    "beta=0.2\n",
    "K=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "dc85e6bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6448536269514722 0.8416212335729143\n"
     ]
    }
   ],
   "source": [
    "z_alpha=stats.norm.ppf(1-alpha)\n",
    "z_beta=stats.norm.ppf(1-beta)\n",
    "print(z_alpha,z_beta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "73a723cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3236021826488815"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigma=df1[df1.landing_page=='new_page']['converted'].std()\n",
    "sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "934fc017",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.03616389114433191"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean=df1[df1.landing_page=='old_page'].groupby(['day']).mean('converted').mean()[1]*0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "64b81b92",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "91.58988724947446"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_size=(1+1/K)*np.power(sigma*(z_alpha+z_beta)/mean,2)\n",
    "sample_size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "ba97ec30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.12054630381443972"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1[df1.landing_page=='old_page'].groupby(['day']).mean('converted').mean()[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1cc904f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def abtest(Dataframe:df1):\n",
    "    standard=df1[df1.landing_page=='old_page'].groupby(['day']).mean('converted').mean()[1]*\n",
    "    df1[df1.landing_page=='new_page'].groupby(['day']).mean('converted').mean()[1]>=1.3*standard\n",
    "    "
   ]
  }
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